Main answer: 12x+39
Supporting answer: Transformation of a graph:
- Transformation of a graph is a graph which involves performing the transformations on the graph's function such as translations and reflections on x and y axis respectively.
- For a given graph we can do transformations and we can find the translations and reflections by performing certain rules:
- Translation of a graph is the graph obtained by adding or subtracting a particular coordinate with the respective function of the graph.
- We can find the translation of a particular graph in vertical stretch by adding or subtracting a particular constant from the y-coordinate.
- We can find the translation of a particular graph in horizontal stretch by adding or subtracting a particular constant from the x-coordinate.
Given to find the transformation of the graph for f(x)=12x-9 by a factor of 4, it can be done in:
f(x)=12x-9
f(x)=12(x+4)-9 as the factor is 4
f(x)=12x+48-9
f(x)=12x+39
as given the transformation is in terms of g we have g(x)=12x+39
Note: It is to be seen whether the graph is in positive or negative axis before taking its transformation, for positive graphs, we add the factor and for negative graphs, we subtract the graphs.
Therefore, the function is g(x)=12x+39.
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